How can I make a line of vertices round?
If you don't mind not using the original vertices, I would add a circle (ShiftA >Add circle) in edit mode, so that it's added straight into the current object.

If you want to keep the existing verts, you could try using the To sphere operator (AltShiftS), or the circle operator in the bundled loop tools addon (you will have to enable in User prefs > Addons).



In the above example I first rotated one of the end verts with proportional editing enabled (O), to give it a semi-circular shape. This makes it easier for the circle operator